1. Field of the Invention
The invention generally relates to a nuclear spectrometer apparatus and method and, in particular, to a nuclear spectrometer that employs unique asymmetrical weighting functions to obtain good energy resolution at high count rates and has especially accurate pulse pile-up detection which is sensitive to the presence of very low energy photon events.
2. Description of Related Art
Photon emission spectra at both X-ray and gamma-ray energies are frequently used in analyzing the elemental composition of materials. Such spectra are generated by measuring the energies of a great number of emitted photons and plotting the number of photons detected against the measured energy. Emission lines characteristic of chemical elements or isotopes appear as peaks in the resulting histogram, and the pattern and heights of these peaks can be used to determine the composition.
One measure of the quality of a nuclear spectrometer system is its energy resolution, which is the degree of spreading of an emission line into a peak of finite width. The lower the width, the better the resolution. At X-ray energies, since the width varies with energy, it is common in the art to specify energy resolution as the width of a particular emission line such as the Mn K-alpha line. Resolution is typically expressed in the art as the so-called Full Width at Half Maximum (FWHM), or the distance in energy between the two points halfway down the peak on either side. Longer pulse shaping times result in improved energy resolution, down to a minimum, or best, resolution determined by the noise characteristics of the detector and preamplifier.
Another figure of merit for a system is throughput, or the number of photons measured per second, which varies with both the incident rate of photon arrival and the pulse shaping time of the spectrometer.
Since photons arrive randomly in time based on Poisson statistics, it is possible for two photons to appear separated by an arbitrarily small time interval. The ability to distinguish between a single photon and two photons arriving close together is known in the art as "pile-up rejection."
A good general description of the prior art for measuring the energies of X-ray photons may be found on pages 296-309 of the book entitled Scanning Electron Microscopy and X-Ray Microanalysis, 2nd edition, by Goldstein, et al. In particular, Goldstein describes the pulse shaping of signals from a semi-conductor detector and preamplifier, and the relationships among shaping times, energy resolution, and pulse pile-up detection.
The traditional technique for prior art pile-up detection is to use one or more short time constant pulse shapers and rely on multiple threshold crossings of the outputs of the "fast channel" shapers with short time constants to detect the occurrence of multiple photons. This has the disadvantage that all conventional pulse shaping begins with differentiating the signal, which accentuates noise, followed by one or more integrations to smooth away the noise. It follows that shorter shaping times have more noise, and thus must have higher thresholds to avoid false triggering due to noise.
Further details of the various known methods of analog pulse shaping in nuclear spectrometers are given by Knoll's book Radiation Detection and Measurement on pages 572-582, and the noise performance of various possible shaping methods is discussed on pages 607-609. Note that the optimum pulse shape for energy resolution is the finite cusp, which is difficult to achieve with analog circuitry.
E. Gatti's and M. Sampietro's paper "Optimum Filters for Detector Charge Measurements in Presence of 1/f Noise," published in Nuclear Instruments and Methods in Physics Research A287 (1990), pp. 513-520, gives a complete theoretical treatment of the noise sources (series and parallel white noise and 1/f noise) for semiconductor photon detectors of the type used in the present invention. Gatti, et al. provides a set of relationships from which an optimum weighting function may be calculated from the noise properties of a semiconductor detector-and preamplifier for both an infinite measurement span and the practical case of a given finite processing interval.
The time-domain weighting function appropriate for use when both parallel white noise and 1/f noise are present (the normal case in a real detector) is described in Gatti, et al.'s paper, using the highest level of 1/f noise discussed in the paper for contrast with a curve of zero 1/f noise. Optimum weighting functions for a real detector fall between the two.
All derivations from classical filter theory which are based on frequency domain noise spectra and signal-to-noise considerations, like Gatti, et al.'s result in time-domain weighting functions which are symmetrical on either side of the photon event and of opposite sign.
U.S. Pat. No. 3,872,287 to Henriecus Koeman describes the application of a symmetrical weighting function to a series of short integrations of the output signal from a detector and preamplifier for equal time periods on either side of a photon step. The Koeman reference also allows the periods to differ from photon to photon, and for the weights to be greater close to the photon step, but always performs his integrations for an equal time period preceding and following each photon step. Since the intervals between photons are generally unequal, this means that some of the integrated samples in the longer interval are not used.
U.S. Pat. No. 5,005,146 to Tamaas Lakatos, et al. describes a very similar system which also relies on symmetric weighting functions and equal time intervals on either side of the photon step. Again, the restriction to equal time intervals necessitates discarding information from the wider interval.
The total error in measuring the height of a step in a noisy signal is the sum of the errors in measuring the signal before and after the step. In statistical terms, the variance of the difference is the sum of the variances of the measurement of the signal level on each side. If more samples can be used on one side of the step, the variance there will be smaller and thus the total variance of the difference will be smaller, improving the accuracy of the energy measurement and improving the resolution as a result. The present invention advantageously relaxes the restriction to equal time periods and symmetric weighting functions in favor of equal areas of the positive and negative sides of the weighting functions, regardless of their width and shape.
The Koeman, et al. patent also discusses the problem of leakage current causing a rising slope in the data stream, leading to an overestimate of the measured energy of a photon step. The remedy described in the Koeman et al. patent is to periodically trigger a measurement when no photon is present and subtract the result from the measured energies. This has two flaws. First, the period over which the zero point is estimated is no longer than the period over which a photon is measured, so random noise causes significant errors in the zero-point estimate. Second, the slope is assumed to be constant. While leakage current may be relatively constant, other sources of apparent slope may vary periodically, such as so-called "microphonics" (low-frequency resonances). The present invention constantly monitors the slope during all times when a step is not detected, averaging over a long period relative to the time of a photon measurement, and dynamically subtracts the average local slope out of the data stream so that the weighting function is applied to a slope-free signal.
U.S. Pat. No. 4,692,626 to Georg P. Westphal discloses a method of measuring the height of a photon step edge which relies on pre-loading the level of the preamplifier output signal prior to the step edge into an accumulator, and then continuously averaging the difference between the samples after the step and that pre-loaded level until the arrival of the next photon. While this technique makes use of all available samples, it does not permit the use of an optimum weighting function for both sides of the photon step. In particular, for the optimum weighting function, a sample will be weighted differently when used to measure the preceding photon than when used to measure the following photon, in order to give higher weight to samples nearer to the photon being measured. The present invention, however, does accomplish this.
The Westphal patent also discusses correction for slope due to leakage current, using the method of differentiating the signal to remove the slowly-varying slope and then subsequently integrating the signal from a zero baseline to generate replicas of the original step with zero slope.
Neither the method of Koeman, et al. nor the method of Westphal compensates well for periodically varying signals such as those produced by microphonic coupling, since they both estimate the correcting signal only from the part of the preamplifier output preceding the photon step. The present invention, by use of appropriate delays, estimates the local slope using a region of the preamplifier output surrounding the photon step and much wider than the processing period of a photon step, thus correcting for both constant and periodically varying slope.
U.S. Pat. No. 5,067,090 to Bronislaw Seeman discloses the use of conventional pulse shaping with a fixed time constant to form the photon step into a roughly Gaussian pulse, followed by fast digitization of the output of the pulse shaping to integrate the area of the pulse. A linear estimate of the baseline of the output of the pulse shaper is made by considering the sample before and after the beginning and end of the pulse, respectively. It is more advantageous to perform the pulse shaping digitally after converting a preamplifier output to digitized form, as is done in the present invention, securing the benefits of optimum filter shaping and pulse-to-pulse variable shaping times for the best combination of resolution and throughput.
Prior art pile-up detection is generally accomplished by using two or more conventional pulse shapers with differing time constants, a very short time constant for good time resolution, but poor energy resolution, and one or more longer time constants for better energy resolution. U.S. Pat. No. 4,152,596 to J. Howard Marshall, III discusses the use of a multiple time-constant approach at gamma-ray photon energies. Three ways of detecting pile-up are disclosed. First, multiple thresholds are used with the fast pulse to increase the chances that two pile-up pulses will produce multiple positive threshold crossings. This will not work unless the two photons are separated by more than the rise time of the fast pulse shaping, so, at best, the pulse-pair rejection timing is improved by about half. Second, the pulse width of the fast channel shaper may be tested against a maximum. Unfortunately, this width varies with energy, and the uncertainty in the width is most severe near the lowest energies distinguishable from noise at the short time constant of the fast channel, where small errors in energy will result in substantial changes in pulse width. Third, the energy from both the fast and slow channels can be measured and tested for equality. If they differ substantially, pile-up may be inferred. This method cannot handle photons too low in energy to be detected at all by the fast channel.
The paper "Optimizing Pulse Pileup Detection for Soft-X-Ray Spectroscopy," written by Alan J. Greenberger and published in Nuclear Instruments and Methods 188 (1981), pp. 125-132, describes a method for detecting pile-up for X-ray energies below 1 KeV. The technique is quite complex, requiring a great deal of circuitry and involving a chi-squared computation which requires an adaptive threshold based on energy to prevent large photons from rejecting themselves. Thus, the pile-up of two low-energy photons is adequately detected, but pile-up of a low-energy photon with a high-energy photon is not. The present invention detects the pile-up of very low energy photons with other such low-energy photons or with higher energy photons, using simple timing relationships to measure the symmetry of the output of a triangle-shaped pulse.
U.S. Pat. No. 4,684,989 to Barbara J. Roeder et al. describes a method for estimating the noise level of a signal having periodic redundant intervals, such as identical pixel locations in the successive frames of the signal from a video camera. In the present invention, there are no predictable redundant intervals due to the random nature of the arrival of photon events, but an estimate of noise level can still be made advantageously by realizing that the interesting parts of the signal are always positive-going steps, and also that the noise is positive-going and negative-going with equal probability. Thus, computing a running sum of only the negative differences between samples separated by a short period of time will yield a reasonable estimate of the local noise level in the signal while automatically ignoring the positive differences caused by photon step edges.
It was in the context of the foregoing prior art that the present invention arose.